Session EM: Nuclear Theory I

Electromagnetic response functions for open-shell nuclei from an ab initio symmetry-adapted framework

We will discuss work with the ab initio symmetry-adapted no-core shell model (SA-NCSM) and the Lanczos response function method to examine intermediate-mass, open-shell nuclei from a first-principle perspective. Using realistic interactions, the SA-NCSM can handle nuclei in ultra-large model spaces by employing symmetries previously shown to dominate the nuclear dynamics. The Lanczos response function method, when combined with the SA-NCSM, allows us to calculate response functions for nuclei and to study their intrinsic dynamics. With a focus on clustering and collectivity, we will present recent results for electromagnetic response functions, including for the open-shell nucleus $^{20}$Ne, discuss the relevant physics, and briefly point to applications for nuclear compressibility.   

Chiral-EFT corrections to Gamow-Teller transitions in light nuclei

Chiral effective field theory ($\chi$EFT) is a framework to systematically derive internucleon interactions, like the LENPIC interaction, and electroweak currents. We have constructed the Gamow-Teller (GT) transition operator from the one-body and two-body weak axial currents. The operator is consistent with the LENPIC interaction up to N2LO. We have applied this operator within the no-core shell model (NCSM) approach to light nuclei. We present preliminary results for the GT transition matrix elements calculated in a harmonic oscillator basis. We also discuss the convergence of the transition matrix elements at each chiral order as function of the basis expansion, and the impact of the $\chi$EFT regulator on the operator.   

Consistent chiral-EFT improved M1 operators for ab initio calculations

Over the past two decades chiral Effective Field Theory ($\chi$EFT) has been successfully applied to model the internucleon interaction, such as the LENPIC interactions, and nuclear electroweak currents to study few nucleon systems. Here we construct the effective M1 operator up to N3LO in a harmonic oscillator (HO) basis consistent with the LENPIC interaction from one-body and two-body $\chi$EFT electromagnetic current operators, and apply that to light nuclei within the framework of the no-core shell model (NCSM). We present preliminary results for the deuteron, 3H and 3He magnetic moments, and study their convergence at each chiral order as function of the basis expansion. We also estimate the chiral truncation uncertainties of these magnetic moments and discuss the role of the $\chi$EFT regulator.   

\textit{Ab initio} M1 observables in the \textit{p}-shell with consistent $\chi\mathrm{EFT}$-improved operators

\textit{Ab initio} methods in nuclear theory strive to make quantitative predictions of nuclear observables, starting with the internucleon interaction. Modern interactions, such as the LENPIC interaction, are derived systematically from chiral effective field theory ($\chi\mathrm{EFT}$). However, the same $\chi\mathrm{EFT}$ treatment used for deriving the potential can be used to derive consistent effective operators for electromagnetic moments and transitions. We have derived the effective M1 operator, consistent with the LENPIC interaction up to N2LO in the chiral expansion, and apply it within the no-core configuration interaction (NCCI) approach for a variety of nuclei in the \textit{p}-shell. We present preliminary results for magnetic moments and M1 transition matrix elements, and explore convergence behavior of the $\chi\mathrm{EFT}$ corrections.   

{\it Ab initio} NCSM One-Body Densities as Input to Effective Potentials for Nucleon-Nucleus Elastic Scattering

Effective interactions ('optical potentials') are needed as input to nuclear reaction calculations. Deriving them {\it ab initio} is a current topic of interest. In a multiple scattering expansion for nucleon-nucleus elastic scattering the lowest order term requires integrating over nonlocal, translationally invariant one-body densities and off-shell nucleon-nucleon (NN) scattering amplitudes. The one-body densities contain a scalar and a vector part when taking into account the spin of the nucleons in the nucleus. However, up to now only the scalar density has been employed when calculating the first order effective potential. \\ In this talk, proton-nucleus elastic scattering observables calculated with effective {\it ab initio} folding potentials based on NCSM scalar and vector one-body densities together with NN amplitudes derived from the same NN interaction will be shown. We will focus on elastic scattering off light nuclei (up to $^{16}$O) in the energy regime between 100 and 200 MeV laboratory kinetic energy.   

Quantum Monte Carlo calculation of scattering in A=4 and A=5 systems

Variational Monte Carlo and Green's function Monte Carlo methods have been applied very successfully to compute energies and other properties of states in light nuclei from quantitatively accurate nucleon-nucleon interactions. However, these calculations have nearly all involved either bound states or else unbound resonance states narrow enough to be approximated as confined systems. The most straightforward application of these methods to nonresonant scattering and reactions is to impose boundary conditions at a spherical surface with fixed separation of the scattering nuclei, and to compute the discrete states inside the confining boundary just like ordinary bound states; the boundary conditions then allow exact continuation of the wave functions into the exterior region, yielding elements of the $S$-matrix. We will describe the application of these methods to neutron scattering from $^4$He and $^3$H nuclei. Spin and orbital angular momentum quantum numbers can change in the latter process, so we are using it as an initial test case to develop coupled-channel calculations. Since the $A=4$ systems are already accurately computed with Faddeev and hyperspherical methods, it will also allow a useful benchmark of our methods before we move on to systems of more nucleons.   

New ab initio approach for nuclear reactions

I will discuss a new ab initio approach for nuclear reactions involving nuclei up to the medium-mass region. This approach is based on the \textit{ab initio} symmetry-adapted framework combined with the resonating group method (RGM). It follows the same concept that has been successfully applied to \textit{ab initio} reactions of light nuclei, but now we take advantage of the SU(3) symmetry. This new feature enables a reorganization of the large-scale model space into physically relevant basis states and paves the way to \textit{ab initio} reactions involving heavier and more exotic nuclei of astrophysical interest. In particular, the nuclear structure of the target is described with the \textit{ab initio} symmetry-adapted no-core shell model, and the target-projectile composite system is described within an SU(3) RGM framework. I will discuss the underlying formalism, which involves the expressions of the norm and Hamiltonian kernels in an SU(3) basis, along with the first applications of the model to one-nucleon projectile reactions. The computational efficacy of the reaction model will be illustrated for a ${}^{20}$Ne target.   

Improved Inelastic Scattering Descriptions for Nuclear Data Evaluations, Nuclear Structure and Reaction Studies

Inelastic scattering reactions play a crucial role for data evaluations. Also, they can potentially be used in surrogate reaction applications, which aim at indirectly determining cross sections for reactions on unstable nuclei, e.g. for nuclear astrophysics simulations. This work aims at improving quantum models for pre-equilibrium reactions. Standard descriptions are based on projectile-target interactions with the reaction inducing a wide energy range of target excitations. The quantum models developed so far are limited to a single particle emission process. We studied various properties of RPA excited states of nuclei. We find the strength functions to be dominated by well-localized particle-hole states. This allows us to determine the proper weight for the p-h transition amplitudes for cross section calculations. We obtained expressions for up to two particles in the continuum for one-step amplitudes, and up to three particles in the continuum for two-step amplitudes. We find simple expressions that allow for a systematic implementation of multiple-particle emission. We present results and discuss the limits of one-step amplitudes. Planned extensions using QRPA structure information for both spherical and deformed nuclei will be considered.   

Nucleon-induced cross-section predictions for deformed nuclei off-stability

Many applications such as astrophysics, nuclear waste management and reactor physics require cross sections and reaction rates that are either unknown or have a scarce availability of experimental data. Therefore, a more predictive approach is needed, encompassing the adoption of more fundamental structure models in the reaction calculations. The strong static deformations of such nuclei off stability limits the reliability of extrapolated global optical model potentials. In this work we address these issues for neutron-induced reactions by extending an adiabatic model that has already been successfully applied to stable deformed rare-earth nuclei to all of their known isotopes off stability. To obtain reliable values for quadrupole and hexadecapole deformation parameters in the cases where such measurements are impractical (or even impossible) we use microscopic Hartree-Fock-Bogoliubov calculations of nuclear densities using the Gogny D1S force, from which observables such as transition probabilities and deformation parameters can be extracted. With this method we were able to obtain reliable cross-section predictions for the whole rare-earth region, from neutron to proton driplines. We also investigate the consistent applicability of this approach to proton-induced reactions.